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Notice that the antiphase density matrix differs from the in-phase representation only in that the sign of the two transitions (e.g., I1 (aI as ^ PI as) and I2 (aI ps ^ PI PS) for the 1H or

I transitions) is opposite. That is the same as saying that the I transition a ^ f (S = a) is 180° out of phase with the I transition a ^ f (S = f). You can "read" the coherences if you focus on the terms below the diagonal. These matrices are in fact the matrix multiplication products of their individual components; for example, 2IxSz is just twice the matrix product of the Ix and Sz matrices.

The products of the x and y operators give the following four matrices:

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